"... Solomonoff's optimal but noncomputable method for inductive inference assumes that observation sequences x are drawn from an recursive prior distribution p(x). Instead of using the unknown p() he predicts using the celebrated universal enumerable prior M() which for all exceeds any recursiv ..."

Solomonoff&apos;s optimal but noncomputable method for inductive inference assumes that observation sequences x are drawn from an recursive prior distribution p(x). Instead of using the unknown p() he predicts using the celebrated universal enumerable prior M() which for all exceeds any recursive p(), save for a constant factor independent of x. The simplicity measure M() naturally implements &quot;Occam&apos;s razor &quot; and is closely related to the Kolmogorov complexity of . However, M assigns high probability to certain data that are extremely hard to compute. This does not match our intuitive notion of simplicity. Here we suggest a more plausible measure derived from the fastest way of computing data. In absence of contrarian evidence, we assume that the physical world is generated by a computational process, and that any possibly infinite sequence of observations is therefore computable in the limit (this assumption is more radical and stronger than Solomonoff&apos;s).

... [9]: Corollary 1 (Unit loss bound). Suppose initial sequence prefixes xn are drawn with true but unknown probability S(x). A system predicts the k q- 1st sequence element, given x, and receives losss=-=[0, 1]-=- depending on the true k q- lst symbol. The As,-system is optimal in the sense that it predicts as to minimize the S-expected loss; As minimizes the S-expected loss. For the first n symbols, the total...

The traditional theory of Kolmogorov complexity and algorithmic probability focuses on monotone Turing machines with one-way write-only output tape. This naturally leads to the universal enumerable Solomono-Levin measure. Here we introduce more general, nonenumerable but cumulatively enumerable measures (CEMs) derived from Turing machines with lexicographically nondecreasing output and random input, and even more general approximable measures and distributions computable in the limit. We obtain a natural hierarchy of generalizations of algorithmic probability and Kolmogorov complexity, suggesting that the &quot;true&quot; information content of some (possibly in nite) bitstring x is the size of the shortest nonhalting program that converges to x and nothing but x on a Turing machine that can edit its previous outputs. Among other things we show that there are objects computable in the limit yet more random than Chaitin&apos;s &quot;number of wisdom&quot; Omega, that any approximable measure of x is small for any x lacking a short description, that there is no universal approximable distribution, that there is a universal CEM, and that any nonenumerable CEM of x is small for any x lacking a short enumerating program. We briey mention consequences for universes sampled from such priors.

...isc, or a never ending evolution of a virtual reality determined by asnite algorithm, such as in Example 2.1? Contrary to a widely spread misunderstanding, quantum physics, quantum computation (e.g., =-=[3]-=-) and Heisenberg's uncertainty principle do not rule this out [35]. In absence of contrarian evidence we might assume our universe is formally describable indeed, or at least sampled from a formally d...

"... Most traditional artificial intelligence (AI) systems of the past 50 years are either very limited, or based on heuristics, or both. The new millennium, however, has brought substantial progress in the field of theoretically optimal and practically feasible algorithms for prediction, search, induct ..."

Most traditional artificial intelligence (AI) systems of the past 50 years are either very limited, or based on heuristics, or both. The new millennium, however, has brought substantial progress in the field of theoretically optimal and practically feasible algorithms for prediction, search, inductive inference based on Occam’s razor, problem solving, decision making, and reinforcement learning in environments of a very general type. Since inductive inference is at the heart of all inductive sciences, some of the results are relevant not only for AI and computer science but also for physics, provoking nontraditional predictions based on Zuse’s thesis of the computer-generated universe.

"... Coupled electron-nuclear spins are promising physical systems for quantum in-formation processing: By combining the long coherence times of the nuclear spins with the ability to initialize, control, and measure the electron spin state, the favor-able properties of each spin species are utilized. Thi ..."

Coupled electron-nuclear spins are promising physical systems for quantum in-formation processing: By combining the long coherence times of the nuclear spins with the ability to initialize, control, and measure the electron spin state, the favor-able properties of each spin species are utilized. This thesis discusses a procedure to initialize these nuclear spin qubits, and presents a vision of how these systems could be used as the fundamental processing unit of a quantum computer. The fo-cus of this thesis is on control of a system in which a single electron spin is coupled to N nuclear spins via resolvable anisotropic hyperfine (AHF) interactions. High-fidelity universal control of this le-Nn system is possible using only excitations on a single electron spin transition. This electron spin actuator control is implemented by using optimal control theory to find the modulation sequences that generate the desired unitary operations. Decoherence and the challenge of making useful qubits from these systems are also discussed. Experimental evidence of control using an electron spin actuator was acquired with a custom-built pulsed electron spin resonance spectrometer. Complex mod-

"... We briefly review recent results in the field of theoretically optimal algorithms for prediction, search, decision making, and reinforcement learning in environments of a very general type. The results may be relevant not only for computer science but also for physics. ..."

We briefly review recent results in the field of theoretically optimal algorithms for prediction, search, decision making, and reinforcement learning in environments of a very general type. The results may be relevant not only for computer science but also for physics.

"... Coherent control is a fundamental challenge in quantum information processing (QIP). Our system of interest employs a local, isolated electron spin to coherently control nuclear spins. Coupled electron/nuclear spins are a promising candidate for QIP: nuclear spins are used for information storage an ..."

Coherent control is a fundamental challenge in quantum information processing (QIP). Our system of interest employs a local, isolated electron spin to coherently control nuclear spins. Coupled electron/nuclear spins are a promising candidate for QIP: nuclear spins are used for information storage and computation due to their long coherence times, while the electron is used as a spin actuator for initialization, information transfer, control, and readout. This is the first implementation of a local processor using the central qubit architecture. In this work, a robust integrated system for coherent control of these spins is proposed. The system includes a mechanical and cryogenic system for sample handling, cooling, and suspension; computer software for experimental control and optimal control pulse determination; and a custom-designed pulsed electron spin resonance (ESR) spectrometer with digital signal acquisition and processing. The spectrometer enhances and expands past contributions of J. S. Hodges and J. C. Yang, who built a first generation device capable of amplitude modulated

...ts the properties of entanglement and superposition in physical systems to solve certain problems, such as factoring and searching an unstructured database, more efficiently than classical processing =-=[2]-=-. Liquid-state molecular ensembles containing nuclear spins were recognized to be promising candidates for quantum bits more than a decade ago [9, 21]. Nuclear magnetic resonance (NMR) has been used t...